The banks and the settlement procedure. We analyze banks’ decision-making by considering the trade-off between the total settlement delay and the total cost of funds. All delayed payments will be set-tled and all accounts will be reset to the reserve level when netting occurs in the last period of the process, and the system will be restarted. We set up an experiment to model the system’s performance. To begin, we assume there are banks, each is subject to settlement periods, and final settlement via netting occurs in the last period. Suppose the system has a settlement period of 6 minutes or 10 times per hour.
Then every 3 hours – which is a long enough period of time to observe system performance – there will be T = 30 periods in which settlement-related decision-making will occur. This frequency can be viewed as near to real-time. Similarly, when T = 15 periods, settlement will occur every 12 minutes, which is still a relatively high frequency of settlement within a 3-hour period of time. We can easily extend these ways of modeling time periods for settlement and final settlement to a full day of operation, without loss of generality. For example, because settlement with netting restarts the whole process, we can simulate 24 hours of system operations by aggregating 8 random instances of our simulation. The qualitative insights remain unchanged this way. So we have limited our coverage to system performance over 3 hours within a day. It is sufficient to demonstrate our essential findings by focusing on system performance across the periods in which settlement occurs up to the final period involving settlement with netting.
Banks receive payment requests that arrive in real time, but only settle periodically. In each settlement period , bank receives random requests to pay bank with probability pi, which we de-note as . If payment requests can be settled directly by the bank within the period, it is considered as an instance of near real-time settlement handled via RTGS. If not, the payment requests will either enter bank ’s internal queue or the intermediary-managed central queue, depending on the system design. In the case of central queue, priorities of payments are set by the banks, but settlement is decided on by the intermediary. Some payments are settled via the intermediary’s RTGS if sufficient liquidity is available, while others are handled via delayed settlements. We further assume that no two payments that go from bank to bank will arrive at the same time. If they arrive together, two payments can be combined into one payment request. Furthermore, we assume each payment request has a delay coefficient , which can be understood as a unit delay cost that measures the sensitivity of delay.
Payment prioritization. If the weighted value of the payment request (the payment amount times the delay cost parameter) is greater than a threshold value , then it will be treated as a high-priority pay-ment; otherwise, it will be considered as a low-priority payment. This approach proxies for the banks’ de-cisions, and this reflects differences in how payments will be handled. Figure C1 illustrates the related payment prioritization rule.
Figure C1. Payment Prioritization Rule
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The bank will settle the high-priority payments as soon as possible in the period when the payment re-quest arrives. So there will be no delay cost incurred for high-priority payments. However, this will some-times lead to an overdraft of the bank’s reserve account at the central bank, with a per unit penalty cost of overdraft . In contrast, low-priority payments will be handled differently based on the bank’s reserve account balance. If funds are available in the account, then the request will be settled in this period; other-wise, the payment will be queued with other unsettled payments in the bank’s internal queue or in the central queue, depending on the mechanism. The queued payments will be selectively settled either by the bank in subsequent periods when funds become available, or by the intermediary. The delayed low-prior-ity payments reduce the possible overdraft cost at the expense of delayed settlement, which is an eco-nomic trade-off.
Each individual bank determines its own threshold level for . In settlement period m, denote the immediate payment set by Pim ={qijt |d qij ijt t ³qi,t=m} and the delayed payment set with
The Case of an Internal Queue. In the case of an internal queue, the banks will solve the following optimization problem in each settlement period :
system. When , the payment request will be settled. As a result, the payment will be removed from the queue and there will be no delay related to this payment. The summation over is bank ’s total delay costs related to its unsettled payments to all other banks. The term dmax(-Bim, 0) is bank ’s over-draft cost in this settlement period, which is incurred only if B <im 0, when bank faces a negative ac-count balance at the end of settlement period . Since is the cumulative measure of bank ’s availa-ble funds, it does not require the summation sign.
The balance constraint specifies bank ’s account balance at the end of settlement period , which should be equal to its account balance at the end of the previous period, , minus the high-priority payments to other banks that must be settled in this period, minus low-priority payments to other banks that are selected to be settled in this period.
The Case of a Central Queue. In the case of a central queue, the settlement intermediary may help the banks to cover the liquidity shortfall in the presence of an imbalance of funds in the system. To give banks an incentive to pay back the central queue in a timely manner, the central queue may charge a fee
per unit for its intertemporal liquidity provision.
Bank will make two decisions. First, it will determine what payments it will settle itself in this pe-riod and what payments should be submitted for queuing. Second, in the case that the bank has an out-standing debt with the central queue, it will decide how much to pay back to the intermediary. The bank’s objective is to minimize the total cost of its payment delay costs up to time in a day, plus the overdraft cost to the central bank and the liquidity cost to the central queue. The objective function is given by:
d
Compared with the decision-making model related to the internal queue, the additional term is the liquidity cost of borrowing from the intermediary if a bank has not repaid all its debt.
The objective function trades off the total payment delay cost, the overdraft penalty cost charged by cen-tral bank, and the liquidity cost of borrowing from the intermediary.
The balance constraint is interpreted similar to that for the internal queue. In addition to the immediate payments and the delayed payments settled in this period, the bank also will consider the repayment to the intermediary. The second constraint states that the amount paid back to the settlement intermediary is no more than the amount the bank owed: no banks keep their cash reserves with the intermediary.
Intermediated settlement. Settlement at the end of each period allows multiple payments to be settled simultaneously, if offsetting funds to match are available. At the end of periods, all payments in the queue will be netted. The intermediary’s objective is to minimize the total delay cost and the cost of bor-rowing from the central queue for all banks in period . It solves the following optimization problem:
(3)
The interpretation of the settlement decision variable is the same as for the internal queue. The ob-jective is to minimize the total payment delay cost and the total borrowing cost from the intermediary for liquidity. The means of doing this is by selecting payments from the central queue to settle without violat-ing the settlement constraints.
The first constraint is the equality that computes the net outgoing payment amount for each bank . It is the total net settlement of bank , which is equal to the total payments bank pays other banks less the total receipts bank obtains from other banks. If , then bank will have a net receipt of funds from the other banks and it will not need to borrow from the intermediary. If , then bank will borrow the amount from the intermediary. However, the second constraint ensures that the total amount borrowed by all banks does not exceed the intermediary’s liquidity pool of funds available, cm, in settlement period m.